4
(a) Let Y have a uniform (0, 1) distribution. What is the probability distribution
of U = −3 ln(Y )?
(b) Let X, Y be jointly continuous random variables with joint density function
given by f (x, y) = 2x on 0 <= x <= 1, 0 <= y <= 1 and f (x, y) = 0 elsewhere. What is Cov(X, Y )?
(c) Random variable Y has moment-generating function m(t) = (1 − 4t)−1 for
t < 1/4 , what is the probability distribution for Y ?